The average highschool teacher salary is 43000 Payscalecom A

The average high-school teacher salary is $43,000 (Payscale.com, August 20, 2010). Let teacher salary be normally distributed with a standard deviation of $18,000.

a) Mr. Lucky has been a teacher only for 2 years. Despite being new as a teacher, his salary is already in the top 5% of all high-school salaries. Mr. Lucky must be making at least how much in salary? Round to 2 decimal places.

b) Mr. Unlucky has been a teacher for over 10 years, but his salary is in the bottom 20% of all high-school salaries. Mr. Unlucky must be making at most how much in salary?Round to 2 decimal places.

Solution

a)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.95      
          
Then, using table or technology,          
          
z =    1.644853627      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    43000      
z = the critical z score =    1.644853627      
s = standard deviation =    18000      
          
Then          
          
x = critical value =    72607.37   [ANSWER]  

******************

b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.2      
          
Then, using table or technology,          
          
z =    -0.841621234      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    43000      
z = the critical z score =    -0.841621234      
s = standard deviation =    18000      
          
Then          
          
x = critical value =    27850.82 [answer]